Efficient and accurate log-Lévy approximations to Lévy driven LIBOR models

Antonis Papapantoleon; John Schoenmakers; David Skovmand

Efficient and accurate log-Lévy approximations to Lévy driven LIBOR models

Antonis Papapantoleon, John Schoenmakers, David Skovmand

Institut for Matematiske Fag

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Abstract

The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a L\'evy-driven LIBOR model and aim at developing accurate and efficient log-L\'evy approximations for the dynamics of the rates. The approximations are based on truncation of the drift term and Picard approximation of suitable processes. Numerical experiments for FRAs, caps, swaptions and sticky ratchet caps show that the approximations perform very well. In addition, we also consider the log-L\'evy approximation of annuities, which offers good approximations for high volatility regimes.

Originalsprog	Engelsk
Tidsskrift	Journal of Computational Finance
ISSN	1460-1559
Status	Udgivet - 5 jun. 2011

Emneord

q-fin.CP
math.PR
q-fin.PR
91G30, 91G60, 60G51

Adgang til dokumentet

1106.0866v2

Citationsformater

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title = "Efficient and accurate log-L{\'e}vy approximations to L{\'e}vy driven LIBOR models",

abstract = "The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a L\'evy-driven LIBOR model and aim at developing accurate and efficient log-L\'evy approximations for the dynamics of the rates. The approximations are based on truncation of the drift term and Picard approximation of suitable processes. Numerical experiments for FRAs, caps, swaptions and sticky ratchet caps show that the approximations perform very well. In addition, we also consider the log-L\'evy approximation of annuities, which offers good approximations for high volatility regimes.",

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author = "Antonis Papapantoleon and John Schoenmakers and David Skovmand",

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T1 - Efficient and accurate log-Lévy approximations to Lévy driven LIBOR models

AU - Papapantoleon, Antonis

AU - Schoenmakers, John

AU - Skovmand, David

N1 - 32 pages, 21 figures. Added an example of a path-dependent option (sticky ratchet caplet). Forthcoming in the Journal of Computational Finance

PY - 2011/6/5

Y1 - 2011/6/5

N2 - The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a L\'evy-driven LIBOR model and aim at developing accurate and efficient log-L\'evy approximations for the dynamics of the rates. The approximations are based on truncation of the drift term and Picard approximation of suitable processes. Numerical experiments for FRAs, caps, swaptions and sticky ratchet caps show that the approximations perform very well. In addition, we also consider the log-L\'evy approximation of annuities, which offers good approximations for high volatility regimes.

AB - The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a L\'evy-driven LIBOR model and aim at developing accurate and efficient log-L\'evy approximations for the dynamics of the rates. The approximations are based on truncation of the drift term and Picard approximation of suitable processes. Numerical experiments for FRAs, caps, swaptions and sticky ratchet caps show that the approximations perform very well. In addition, we also consider the log-L\'evy approximation of annuities, which offers good approximations for high volatility regimes.

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KW - math.PR

KW - q-fin.PR

KW - 91G30, 91G60, 60G51

M3 - Journal article

SN - 1460-1559

JO - Journal of Computational Finance

JF - Journal of Computational Finance

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